Hi,
It is possible to register for Self Assessment without a National Insurance number. Details on how to do this can be found here:
Check how to register for Self Assessment
If you need to setup a personal tax you will need to verify your identity once you have registered with the gateway.
However, you need a National Insurance number to make sure your NI Contributions and tax are recorded against your name only. If you do not have an National Insurance number you can apply for one here:
Apply for a National Insurance number
If you have lost your National Insurance number you can use the guidance here to find it:
Find your National Insurance number
Thank you.